For each of the following statements, clearly state if it is true or false.

Moreover, provide either a counterexample if the statement is false or a

brief justication if the statement is true.

(i) If a system is consistent, removing one of its equation results in a new

system that is inconsistent.

(ii) If the columns of an mn matrix span Rm, adding one more column

to the matrix results in a matrix whose columns span Rm.

(iii)If u; v are linear dependent vectors in R4, then u; 2u - v are linearly

dependent.